An analyst would like to construct 95% confidence intervals for the mean stock returns in two industries. Industry A is a high-risk industry with a known population standard deviation of 20.6%, whereas Industry B is a lower-risk industry with a known population standard deviation of 12.8%.

a. What is the minimum sample size required by the analyst if she wants to restrict the margin of error to 4% for Industry A?

b. What is the minimum sample size required by the analyst if she wants to restrict the margin of error to 4% for Industry B?

c. Why do the above results differ if they use the same margin of error?